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Motion in One Dimension

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Presentation on theme: "Motion in One Dimension"— Presentation transcript:

1 Motion in One Dimension
Chapter 2 Motion in One Dimension

2 Dynamics The branch of physics involving the motion of an object and the relationship between that motion and other physics concepts Kinematics is a part of dynamics In kinematics, you are interested in the description of motion Not concerned with the cause of the motion

3 Quantities in Motion Any motion involves 3 concepts Displacement
Velocity Acceleration

4 Brief History of Motion
Sumaria and Egypt Mainly motion of heavenly bodies Greeks Also to understand the motion of heavenly bodies Systematic and detailed studies Geocentric model

5 “Modern” Ideas of Motion
Copernicus Developed the heliocentric system Galileo Made astronomical observations with a telescope Experimental evidence for description of motion Quantitative study of motion

6 Position Defined in terms of a frame of reference
One dimensional, so generally the x- or y-axis Defines a starting point for the motion

7 Displacement Defined as the change in position
f stands for final and i stands for initial May be represented as y if vertical Units are meters (m) in SI, In your book, moving to the right is deemed positive direction and to the left is negative direction

8 Displacements

9 Vector and Scalar Quantities
Vector quantities need both magnitude and direction to completely describe them Generally denoted by boldfaced type and an arrow over the letter + or – sign is sufficient for this chapter Scalar quantities are completely described by magnitude only

10 Displacement Isn’t Distance
The displacement of an object is not the same as the distance it travels Example: Throw a ball straight up and then catch it at the same point you released it The distance is twice the height The displacement is zero

11 Speed The average speed of an object is defined as the total distance traveled divided by the total time elapsed Speed is a scalar quantity

12 Speed, cont Average speed totally ignores any variations in the object’s actual motion during the trip The total distance and the total time are all that is important SI units are m/s

13 Velocity It takes time for an object to undergo a displacement
The average velocity is rate at which the displacement occurs generally use a time interval, so let ti = 0

14 Velocity continued Direction will be the same as the direction of the displacement (time interval is always positive) + or - is sufficient Units of velocity are m/s (SI) Velocity is a vector quantity It is the speed PLUS direction

15 Speed vs. Velocity Cars on both paths have the same average velocity since they had the same displacement in the same time interval The car on the blue path will have a greater average speed since the distance it traveled is larger

16 Graphical Interpretation of Velocity
Velocity can be determined from a position-time graph Average velocity equals the slope of the line joining the initial and final positions An object moving with a constant velocity will have a graph that is a straight line

17 Average Velocity, Constant
The straight line indicates constant velocity The slope of the line is the value of the average velocity

18 Average Velocity, Non Constant
The motion is non-constant velocity The average velocity is the slope of the blue line joining two points

19 Instantaneous Velocity
The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero The instantaneous velocity indicates what is happening at every point of time

20 Instantaneous Velocity on a Graph
The slope of the line tangent to the position-vs.-time graph is defined to be the instantaneous velocity at that time The instantaneous speed is defined as the magnitude of the instantaneous velocity

21 Uniform Velocity Uniform velocity is constant velocity
The instantaneous velocities are always the same All the instantaneous velocities will also equal the average velocity

22 On your own or in groups.. Let’s review the hw from Monday night, then
In your book, complete page 44 # 5 & 6 And page 47 # 1-2 and 4-6

23 Acceleration Changing velocity (non-uniform) means an acceleration is present Acceleration is the rate of change of the velocity Units are m/s²

24 Average Acceleration Vector quantity
When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing

25 Instantaneous Acceleration
The limit of the average acceleration as the time interval goes to zero When the instantaneous accelerations are always the same, the acceleration will be uniform The instantaneous accelerations will all be equal to the average acceleration

26 Graphical Interpretation of Acceleration
Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph

27 Average Acceleration

28 Relationship Between Acceleration and Velocity
Uniform velocity (shown by red arrows maintaining the same size) Acceleration equals zero

29 Relationship Between Velocity and Acceleration
Velocity and acceleration are in the same direction Acceleration is uniform (blue arrows maintain the same length) Velocity is increasing (red arrows are getting longer) Positive velocity and positive acceleration

30 Relationship Between Velocity and Acceleration
Acceleration and velocity are in opposite directions Acceleration is uniform (blue arrows maintain the same length) Velocity is decreasing (red arrows are getting shorter) Velocity is positive and acceleration is negative

31 Kinematic Equations Used in situations with uniform acceleration

32 Notes on the equations Gives displacement as a function of velocity and time Use when you don’t know and aren’t asked for the acceleration

33 Notes on the equations Shows velocity as a function of acceleration and time Use when you don’t know and aren’t asked to find the displacement

34 Graphical Interpretation of the Equation

35 Notes on the equations Gives displacement as a function of time, velocity and acceleration Use when you don’t know and aren’t asked to find the final velocity

36 Notes on the equations Gives velocity as a function of acceleration and displacement Use when you don’t know and aren’t asked for the time

37 Problem-Solving Hints
Read the problem Draw a diagram Choose a coordinate system, label initial and final points, indicate a positive direction for velocities and accelerations Label all quantities, be sure all the units are consistent Convert if necessary Choose the appropriate kinematic equation

38 Problem-Solving Hints, cont
Solve for the unknowns You may have to solve two equations for two unknowns Check your results Estimate and compare Check units

39 Now complete: Page 58 # 3,4,5 Page 59 # 1-6

40 Galileo Galilei Galileo formulated the laws that govern the motion of objects in free fall Also looked at: Inclined planes Relative motion Thermometers Pendulum

41 Free Fall All objects moving under the influence of gravity only are said to be in free fall Free fall does not depend on the object’s original motion All objects falling near the earth’s surface fall with a constant acceleration The acceleration is called the acceleration due to gravity, and indicated by g

42 Acceleration due to Gravity
Symbolized by g g = 9.80 m/s² When estimating, use g » 10 m/s2 g is always directed downward toward the center of the earth Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion moon video

43 Kinematic Equations Same equations used for free fall

44 Free Fall – an object dropped
Initial velocity is zero Let up be positive Use the kinematic equations Generally use y instead of x since vertical Acceleration is g = m/s2 vo= 0 a = g

45 Free Fall – an object thrown downward
a = g = m/s2 Initial velocity  0 With upward being positive, initial velocity will be negative

46 Free Fall -- object thrown upward
Initial velocity is upward, so positive The instantaneous velocity at the maximum height is zero a = g = m/s2 everywhere in the motion v = 0

47 Thrown upward, cont. The motion may be symmetrical
Then tup = tdown Then v = -vo The motion may not be symmetrical Break the motion into various parts Generally up and down

48 Need to divide the motion into segments
Possibilities include Upward and downward portions The symmetrical portion back to the release point and then the non-symmetrical portion

49 Combination Motions

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